Topology optimization design of frequency- and temperature-dependent viscoelastic shell structures under non-stationary random excitation

This paper investigates the topology optimization design of viscoelastic planar shell structures to minimize the random vibration intensity under non-stationary random excitation. The excitation is is modeled as uniformly modulated evolutionary random process. The viscoelastic material is characterized using the Golla Hughes McIavish (GHM) model, and dissipative coordinates are introduced to construct the augmented system equations. To measure the intensity of random responses, the averaged power spectral density (PSD) of the displacement response over a specific frequency band and time interval is considered as the design objective and solved by a scheme that combines the pseudo excitation method (PEM) and the high precision direct (HPD) integration method. The relative density of the viscoelastic material is the design variable. The density-based approach is employed to achieve the optimal distribution. Sensitivity analysis is performed to obtain gradient information. The proposed method is verified through numerical simulation. In addition, the effects of frequency band, time interval, ambient temperature and multiple excitations on the optimization results are also discussed.